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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 5776.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5776.d1 | 5776o2 | \([0, -1, 0, -404440, -109454224]\) | \(-37966934881/4952198\) | \(-954288200894210048\) | \([]\) | \(86400\) | \(2.1832\) | |
| 5776.d2 | 5776o1 | \([0, -1, 0, -120, 520816]\) | \(-1/608\) | \(-117161556574208\) | \([]\) | \(17280\) | \(1.3784\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5776.d have rank \(1\).
Complex multiplication
The elliptic curves in class 5776.d do not have complex multiplication.Modular form 5776.2.a.d
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
